Classical Artificial Neural Network Training Using Quantum Walks as a Search Procedure

• Published in: arXiv.org
• Main Authors: de Souza, Luciano S, Jonathan H A de Carvalho, Ferreira, Tiago A E
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 02.09.2021
• Subjects: Algorithms; Artificial neural networks; Back propagation; Back propagation networks; Machine learning; Neural networks; Physics - Quantum Physics; Quantum computing; Search algorithms
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2108.12448

This paper proposes a computational procedure that applies a quantum algorithm to train classical artificial neural networks. The goal of the procedure is to apply quantum walk as a search algorithm in a complete graph to find all synaptic weights of a classical artificial neural network. Each vertex of this complete graph represents a possible synaptic weight set in the \(w\)-dimensional search space, where \(w\) is the number of weights of the neural network. To know the number of iterations required \textit{a priori} to obtain the solutions is one of the main advantages of the procedure. Another advantage is that the proposed method does not stagnate in local minimums. Thus, it is possible to use the quantum walk search procedure as an alternative to the backpropagation algorithm. The proposed method was employed for a \(XOR\) problem to prove the proposed concept. To solve this problem, the proposed method trained a classical artificial neural network with nine weights. However, the procedure can find solutions for any number of dimensions. The results achieved demonstrate the viability of the proposal, contributing to machine learning and quantum computing researches.